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Collaborating Authors
Hirasaki, George
Mobility of Ethomeen C12 and Carbon Dioxide (CO2) Foam at High Temperature/High Salinity and in Carbonate Cores
Cui, Leyu (Rice University) | Ma, Kun (Rice University) | Puerto, Maura (Rice University) | Abdala, Ahmed A. (Petroleum Institute at Abu Dhabi) | Tanakov, Ivan (Rice University) | Lu, Lucas J. (Rice University and Petroleum Institute at Abu Dhabi) | Chen, Yunshen (University of Texas at Austin) | Elhag, Amro (University of Texas at Austin) | Johnston, Keith P. (University of Texas at Austin) | Biswal, Sibani L. (Rice University) | Hirasaki, George (Rice University)
Summary The low viscosity and density of carbon dioxide (CO2) usually result in the poor sweep efficiency in CO2-flooding processes, especially in heterogeneous formations. Foam is a promising method to control the mobility and thus reduce the CO2 bypass because of the gravity override and heterogeneity of formations. A switchable surfactant, Ethomeen C12, has been reported as an effective CO2-foaming agent in a sandpack with low adsorption on pure-carbonate minerals. Here, the low mobility of Ethomeen C12/CO2 foam at high temperature (120 °C), high pressure (3,400 psi), and high salinity [22 wt% of total dissolved solids (TDS)] was demonstrated in Silurian dolomite cores and in a wide range of foam qualities. The influence of various parameters, including aqueous solubility, thermal and chemical stability, flow rate, foam quality, salinity, temperature, and minimum-pressure gradient (MPG), on CO2 foam was discussed. A local-equilibrium foam model, the dry-out foam model, was used to fit the experimental data for reservoir simulation.
- Asia (1.00)
- North America > United States > Texas (0.28)
- Geology > Mineral (1.00)
- Geology > Rock Type > Sedimentary Rock > Carbonate Rock (0.48)
Experimentally-Based Empirical Foam Modeling
Abbaszadeh, Maghsood (Innovative Petrotech Solutions) | Nia Korrani, Aboulghasem Kazami (Innovative Petrotech Solutions) | Lopez-Salinas, Jose Luis (Rice U.) | Rodriguez-de la Garza, Fernando (PEMEX E&P) | Villavicencio Pino, Antonio (PEMEX E&P) | Hirasaki, George (Rice U.)
Abstract This paper presents fine-scale numerical simulations and mathematical analysis of the empirical foam model for representing foam-surfactant flow in a vertical column of laboratory sand-pack based on two sets of experimental data conducted at variable total velocities and variable foam qualities.The empirical foam model of CMG-STASRS is used for parametric matching of laboratory data, and relevant foam parameters are calibrated.The paper discusses experimental setup, procedure and measurements to provide apparent foam viscosity data needed for foam modeling. In the first set of lab tests, foam quality is constant and the total fluid superficial velocity varies for foam shear thinning effect; while in the second tests, foam quality is varied at a fixed total superficial velocity to capture different flow regimes and foam dry-out characteristics.Employing an analytical method and 1-D numerical simulations of the foam flow in the sand-pack, the empirical foam model is tuned to the first data set of variable velocity and used to predict the second data set of variable quality as a consistency check.The model predictions for the second data set as well as the associated sensitivity analysis prove that the foam modeling procedure of this paper is unique and applicable for large-scale predictions.
- Europe (0.67)
- North America > United States > Texas (0.46)
- North America > United States > California (0.46)
- North America > United States > Oklahoma (0.29)
- North America > Mexico > Gulf of Mexico > Bay of Campeche > Sureste Basin > Campeche Basin > Northeast Marine Region > Cantarell Field (0.99)
- Europe > Norway > North Sea > Northern North Sea > East Shetland Basin > PL 375 > Block 34/7 > Snorre Field > Statfjord Group (0.99)
- Europe > Norway > North Sea > Northern North Sea > East Shetland Basin > PL 375 > Block 34/7 > Snorre Field > Lunde Formation (0.99)
- (10 more...)
Core And Log Nmr Measurements Indicate Reservoir Rock Is Altered By Obm Filtrate.
Shafer, John (Reservoir Management Group) | Chen, Jiansheng (Rice University) | Flaum, Mark (Rice University) | Hirasaki, George (Rice University) | Boyd, Austin (Schlumberger-Doll Research) | Straley, Christian (Schlumberger-Doll Research) | Borbas, Tim (ConocoPhillips) | Devier, Chuck (PTS Labs)
ABSTRACT A core-to-log NMR calibration program for a Gulf of Mexico deep-water reservoir indicates the near wellbore rock wettability is intermediate-wet to oil-wet with enhanced relaxation that results in significant internal gradients (150 to 200 Gauss/cm). This affects the validity of certain aspects of NMR well log interpretation because the response is usually based on the assumption that the formation is water-wet and the magnetic field gradient is equal to that designed for the logging tool. NMR logs were obtained on nine wells including the cored well and logging-while-drilling (LWD) NMR on an offset well followed by about a week later by wireline NMR log. LWD NMR wiper pass logs run 2.5 days after drilling indicate a longer relaxing T2 peak than the wireline log run 7 days after drilling. These observations are consistent with the OBMF filtrate invasion of the formation causing enhanced relaxation of the OBMF by wettability alteration and paramagnetic particle invasion. Fresh state and OBMF at Swi (connate water) core plug saturation states have NMR T2 distributions at reservoir confining stress and temperature similar to the wireline log NMR over the same depth intervals. Cores at Swi saturated with OBMF have oil relaxation rates much faster than the bulk OBMF relaxation rate and the OBMF T2 mode in the cores does not vary significantly with temperature. Both of these observations indicate that the main mechanisms for oil relaxation are surface relaxation and internal gradients and indicating oil is wetting some portion of the rock surface. The T1 and T2 distributions of the OBMF depend on whether the whole mud is pressed or a supernatant is filtered. The filtered OBMF was found to contain 0.08 micron paramagnetic particles. Diffusion editing and CPMG T2 distributions with multiple echo spacings indicate high internal gradients, in the range of 50 to 100 G/cm for extracted plugs and over 150 G/cm for fresh-state plugs. Thin sections and SEM photomicrographs and XRD show that the rocks often contain ?trains? of heavy minerals (iron minerals) and shale laminations with little evidence of dispersed clays. The drilling mud solids had a high magnetic susceptibility and the magnetic fraction was identified to contain both iron and magnetite. There is ample evidence the fast relaxation of OBMF is a result of diffusion relaxation with large internal gradients and surface relaxation caused by OBMF alteration. Laboratory investigation is ongoing to determine whether the alteration is caused by the OBM surfactant additives or submicon paramagnetic particulate material in the OBMF.A core-to-log NMR calibration program for a Gulf of Mexico deep-water reservoir indicates the near wellbore rock wettability is intermediate-wet to oil-wet with enhanced relaxation that results in significant internal gradients (150 to 200 Gauss/cm). This affects the validity of certain aspects of NMR well log interpretation because the response is usually based on the assumption that the formation is water-wet and the magnetic field gradient is equal to that designed for the logging tool. NMR logs were obtained on nine wells including the cored well and logging-while-drilling (LWD) NMR on an offset well followed by about a week later by wireline NMR log. LWD NMR wiper pass logs run 2.5 days after drilling indicate a longer relaxing T2 peak than the wireline log run 7 days after drilling. These observations are consistent with the OBMF filtrate invasion of the formation causing enhanced relaxation of the OBMF by wettability alteration and paramagnetic particle invasion. Fresh state and OBMF at Swi (connate water) core plug saturation states have NMR T2 distributions at reservoir confining stress and temperature similar to the wireline log NMR over the same depth intervals. Cores at Swi saturated with OBMF have oil relaxation rates much faster than the bulk OBMF relaxation rate and the OBMF
- Europe > Norway > Norwegian Sea (0.54)
- North America > United States > Texas > Harris County > Houston (0.28)
- Geology > Mineral > Silicate (1.00)
- Geology > Rock Type > Sedimentary Rock > Clastic Rock > Mudrock > Shale (0.34)
- Energy > Oil & Gas > Upstream (1.00)
- Materials > Chemicals > Commodity Chemicals > Petrochemicals (0.46)
Summary Oil recovery by waterflooding in fractured formations is often dependent on spontaneous imbibition. However, spontaneous imbibition is often insignificant in oil-wet, carbonate rocks. Sodium carbonate and anionic surfactant solutions are evaluated for enhancing oil recovery by spontaneous imbibition from oil-wet carbonate rocks. Crude-oil samples must be free of surface-active contaminants to be representative of the reservoir. Calcite, which is normally positively charged, can be made negative with sodium carbonate. The ease of wettability alteration is a function of the aging time and temperature and the surfactant formulation. Introduction Much oil remains in fractured, carbonate oil reservoirs after waterflooding and in some cases in paleotransition zones, which result from the oil/water contact moving upward before discovery. The high remaining oil saturation is caused by a combination of poor sweep in fractured reservoirs and the formation being preferentially oil-wet during imbibition. ("Imbibition" is defined as the process of water displacing oil. "Spontaneous imbibition" is defined as imbibition that takes place by action of capillary pressure and/or buoyancy when a core sample or matrix block is surrounded by brine.) Poor sweep is not an issue in paleotransition zones, but the remaining oil saturation may still be significant. There are several reasons for high remaining oil saturation in fractured, oil-wet, carbonate formations. If the formation is preferentially oil-wet, the matrix will retain oil by capillarity, and high oil saturation transition zones will exist where the upward oil film flow path is interrupted by fractures. This is illustrated in Fig. 1, which shows the oil retained by oil-wet capillaries of different radii. The height of the capillary retained oil column is proportional to the product of IFT and cosine of the contact angle and is inversely proportional to the capillary radius. In oil-wet systems, oil is the phase contacting the rock surfaces, and surface trapping is likely to be particularly important in rocks with highly irregular surfaces and large surface areas (Fig. 2). The objective of this investigation is to develop a process to overcome the mechanisms for oil retention illustrated by Figs. 1 and 2. Oil is retained by wettability and capillarity. Thus, by altering the wettability to preferentially water-wet conditions and reducing the IFT to ultralow values, the forces that retain oil can be overcome. Introducing an injected fluid into the matrix of a fractured formation is challenging because the injected fluid will flow preferentially in the fractures rather than through the matrix. Therefore, the process must be designed to cause spontaneous imbibition of the injected fluid from the fracture system into the matrix, as illustrated in Fig. 3. Spontaneous imbibition by capillarity may no longer be significant because of low IFT. However, if wettability is altered to preferentially water-wet conditions and/or capillarity is diminished through ultralow IFTs, buoyancy will still tend to force oil to flow upward and out of the matrix into the fracture system. The injected fluid in the fractures will replace the displaced oil in the matrix, and therefore the invasion of the injected fluid into the matrix will continue as long as oil flows out of the matrix. Spontaneous imbibition by capillarity is an important mechanism in oil recovery from fractured reservoirs. A recent survey by Morrow and Mason reviews the state-of-the-art. They state that spontaneous imbibition rates with different wettability can be several orders of magnitude slower, and displacement efficiencies range from barely measurable to better than very strongly water-wet. The primary driving force for spontaneous imbibition in strongly water-wet conditions is usually the capillary pressure. Reduction of IFT reduces the contribution of capillary imbibition. Buoyancy, as measured by the product of density difference and the acceleration of gravity, then becomes the dominant parameter governing the displacement, even if oil is the wetting phase. Application of surfactants to alter wettability and thus enhance spontaneous imbibition has been investigated by Austad et al. with chalk and dolomite cores. Chen et al. investigated enhanced spontaneous imbibition with nonionic surfactants. Spinler et al. evaluated 46 surfactants for enhanced spontaneous imbibition in chalk formations. Standnes et al. and Chen et al. used either nonionic or cationic surfactant with a strategy to alter wettability but avoided ultralow tensions. The work presented here differs from the previous work in that sodium carbonate and anionic surfactants are used to both alter wettability and reduce IFT to ultralow values. The primary recovery mechanism in this work is buoyancy or gravity drainage. Wettability alteration and ultralow IFTs are designed to minimize the oil-retention mechanisms. Crude-Oil Samples It is important to have a representative crude-oil sample when designing an EOR process. Because the process is based on surface phenomena, it is important that the crude oil is free of surface-active materials such as emulsion breaker, scale inhibitor, or rust inhibitor. A simple test for contamination is to measure the interfacial tension (IFT) of the crude-oil sample with synthetic brine. Fig. 4 is a plot of the oil/brine IFT of several crude-oil samples from the same field. These measurements were made with a pendant drop apparatus with automatic video data acquisition and fit to the Young-Laplace equation. Samples MY1 and MY2 have low initial IFT that further decreases with time. This is an indication that these samples contain a small amount of surface-active material, which slowly diffuses to the interface and reduces the IFT. Samples MY3 through MY6 have a much larger initial IFT. Even though there is some decrease in IFT with time, the IFT remains in the range of 20 to 30 mN/m. Some early experiments were made with MY1 before we were aware of the contamination, but the later experiments were made with MY3. The properties of the crude-oil samples are listed in Table 1. The higher acid number and viscosity for MY1 compared with the other samples suggest that it may be an outlier. The wettability of the oil samples were compared by pressing an oil drop in brine against a calcite (marble) or glass plate for 5 to 10 minutes, withdrawing the drop, and measuring the water-advancing contact angle after motion has ceased. The water-advancing contact angles of MY1 and MY3 against calcite or glass after aging time of 5 to 10 minutes are compared in Fig. 5. Clearly, MY1 and MY3 crude oils have different wettability properties.
- North America > United States (1.00)
- Asia > China (1.00)
- Europe > Norway > Norwegian Sea (0.64)
- Geology > Mineral > Carbonate Mineral > Calcite (0.68)
- Geology > Rock Type > Sedimentary Rock > Carbonate Rock > Dolomite (0.35)
- Energy > Oil & Gas > Upstream (1.00)
- Materials > Chemicals > Commodity Chemicals > Petrochemicals (0.46)
- Asia > China > Xinjiang Uyghur Autonomous Region > Junggar Basin > Karamay Field (0.99)
- Asia > China > Shandong > Bohai Basin > North China Basin > Gudong Field (0.99)
- Asia > China > Shandong > Bohai Basin > Jiyang Basin > Gudong Field (0.99)
- (2 more...)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Naturally-fractured reservoirs (1.00)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Carbonate reservoirs (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Waterflooding (1.00)
- (2 more...)
Abstract Oil recovery by water flooding in fractured formations is often dependent on spontaneous imbibition. However, spontaneous imbibition is usually insignificant in oil-wet, carbonate rocks. Sodium carbonate and anionic surfactant solutions are evaluated for enhancing oil recovery by spontaneous imbibition from oil-wet carbonate rocks. Crude oil samples must be free of surface-active contaminants to be representative of the reservoir. Calcite, which is normally positively charged, can be made negative with sodium carbonate. The ease of wettability alteration is a function of the aging time and temperature and the surfactant formulation. Introduction Much oil remains in fractured, carbonate oil reservoirs after waterflooding and in some cases in paleo-transitions zones, which result from the oil/water contact moving upward before discovery. The high remaining oil saturation is due to a combination of poor sweep in fractured reservoirs and the formation being preferentially oil-wet during imbibition1,2. Poor sweep is not an issue in paleo-transition zones but yet the remaining oil saturation may still be significant. There are several reasons for high remaining oil saturation in fractured, oil-wet, carbonate formations. Poor sweep was mentioned earlier. If the formation is preferentially oil-wet, the matrix will retain oil similar to an oil-wet blotter and high oil saturation transition zones will exist where the upward oil film flow path is interrupted by fractures. This is illustrated in Fig. 1, which shows the oil retained by oil-wet capillaries of different radii. The height of the capillary retained oil column is greater for the smaller pores. In oil-wet systems, oil is the phase contacting rock surfaces, and surface trapping is likely to be particularly important in rocks with highly irregular surfaces and large surface areas, Fig. 2. The objective of this investigation is to develop a process to overcome the mechanisms for oil retention illustrated by Figs. 1 & 2. Oil is retained by wettability and capillarity. Thus altering the wettability to preferentially water-wet conditions and reducing the interfacial tension to ultra-low values can overcome these mechanisms. Introducing an injected fluid into the matrix of a fractured formation is challenging because the injected fluid will flow preferentially in the fractures rather than through the matrix. Thus the process must spontaneously imbibe the injected fluid from the fracture system into the matrix, as illustrated in Fig. 3. Spontaneous capillary imbibition may no longer be important because of low interfacial tension. However, if wettability is altered to preferentially water-wet and/or capillarity is diminished through ultra-low interfacial tensions, buoyancy will tend to allow oil to flow upward and out of the matrix into the fracture system. The injected fluid will replace the displaced oil in the matrix and thus the spontaneous imbibition will continue as long as oil flows out of the matrix. Spontaneous imbibition is an important mechanism in oil recovery from fracture reservoirs. A recent survey by Morrow and Mason reviews the state-of-the-art. They state that imbibition rates with different wettability can be several orders of magnitude slower and displacement efficiencies range from barely measurable to better than very strongly water-wet. The primary driving force for imbibition in strongly water-wet conditions is the capillary pressure. Reduction of interfacial tension reduces the contribution of capillary imbibition. Buoyancy, as measured by the Bond number then becomes the dominant parameter governing the displacement, even of the wetting phase. Application of surfactant to alter wettability and thus enhance spontaneous imbibition has been investigated by Austad, et al. with chalk and dolomite cores. Chen, et al., investigated enhanced imbibition with nonionic surfactants. Spinler, et al., evaluated 46 surfactants for enhanced imbibition in chalk formations. Standes, et al. and Chen, et al. used either nonionic or cationic surfactant with a strategy to alter wettability but avoiding ultra-low tensions. The work presented here differs from the previous work in that sodium carbonate and anionic surfactants are used to alter wettability and reduce interfacial tension to ultra-low values.
- Asia > China (1.00)
- Europe > Norway > Norwegian Sea (0.64)
- North America > United States > Texas > Harris County > Houston (0.28)
- Geology > Mineral (1.00)
- Geology > Rock Type > Sedimentary Rock > Carbonate Rock > Dolomite (0.35)
- Energy > Oil & Gas > Upstream (1.00)
- Materials > Chemicals > Commodity Chemicals > Petrochemicals (0.46)
- North America > United States > Wyoming > Kiehl Field (0.99)
- North America > United States > California > Sacramento Basin > 4 Formation (0.99)
- Asia > China > Xinjiang Uyghur Autonomous Region > Junggar Basin > Karamay Field (0.99)
- (4 more...)
- Reservoir Description and Dynamics > Unconventional and Complex Reservoirs > Carbonate reservoirs (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Waterflooding (1.00)
- Reservoir Description and Dynamics > Improved and Enhanced Recovery > Chemical flooding methods (1.00)
- Reservoir Description and Dynamics > Formation Evaluation & Management (1.00)
Introduction The 1984 Natl. Petroleum Council (NPC) evaluation of domestic EOR potential stands as the most extensive analysis of the U.S. potential EOR resource ever completed. potential EOR resource ever completed. Publication of the study culminated a 2-year, Publication of the study culminated a 2-year, 50-person-year effort. EOR experts from industry, universities, and government participated. The findings of this study have been participated. The findings of this study have been widely reported, critiqued, and used throughout the industry. L.F. Elkins previously discussed the series of SPE articles on the NPC results by offering his alternative interpretations of the NPC methods and results. He concluded that the methods used in the study were in error; ". . the permeability variations used in the NPC study are anomalous and exceedingly high." He also states that" . . the analyses made by the NPC task force overstate the amounts of remaining oil in place that are trapped in lower-permeability parts of sandstone reservoirs that are within the active dynamic waterfloods. "He concludes this on the basis of his interpretation that the volumetric estimates used in the analysis overstated initial oil in place." These three objections provide the core of his criticism of the NPC analysis. This reply clarifies the NPC's approach and also attempts to clarify several points raised by Elkins concerning the study procedures, models, and data. procedures, models, and data. NPC Data Sources and Procedures The NPC assembled detailed reservoir data and engineering-based models to project possible EOR production under a variety of possible EOR production under a variety of cases reflecting the oil price and the state of technology development. The data-collection effort started with the information available from existing sources within the U.S. DOE, but was significantly expanded and enhanced during the study. Additional material was obtained from questionnaires completed by 18 different companies on 1,300 reservoirs. Table R-1 lists the data elements collected and used in the models. This information was assembled, to the extent available, for each reservoir in the data base. Once collected, all data were thoroughly screened and evaluated for in ternal consistency and were cross-checked with other reservoir properties, companyprovided data, and average values for other reservoirs in the region. For data elements that could not be readily and consistently determined from available data sources, the committees chose to develop default procedures. Where possible, these values were estimated from other data by use of correlations. After all changes were complete, the entire updated data base was again thoroughly screened by committees assigned to assess the potential for the specific EOR methods evaluated. The three committees were composed of renowned experts on miscible flooding, chemical processes, and thermal recovery. Each processes, and thermal recovery. Each committee, in addition to the coordinating committee, included representatives from the oil industry, universities, and government agencies. This effort resulted in the most complete, usable data base possible while guaranteeing internal consistency. The resulting data base contained rock, fluid, geologic, and production information on more than 2,500 reservoirs originally containing more than 330 billion bbl [52.5 × 10–9) M3] Of oil, more than 70% of the national total estimated by the API in 1980. Because of time constraints, the data base was pared to consider only reservoirs with original oil in place (OOIP) estimated at more than 50 million bbl [7.9 × 106 M3]. As a result, the evaluation considered just over 1,000 reservoirs, accounting for more than two-thirds of the total domestic OOIP, a total of around 309 billion bbl [49.1 × 10–9 M3]. Because results were not extrapolated beyond the reservoirs specifically analyzed in this study, they are conservative estimates of the true national EOR potential. The miscible and chemical flooding prediction models required an estimate of the prediction models required an estimate of the permeability variation for each analyzed permeability variation for each analyzed reservoir. Fewer than 50 reservoirs in the data base had values reported for the coefficient of permeability variation. The supplied values were subjective because how they were obtained from core analysis data was not known-e.g., whether the permeabilities were arranged in sequence or averaged permeabilities were arranged in sequence or averaged by position. Because reservoir heterogeneities are unique to each reservoir and directly affect the waterflood as well as the EOR process performance, it was decided to process performance, it was decided to estimate the permeability variation from the demonstrated waterflood recovery performance. performance. The approach used for estimating the Dykstra-Parsons coefficient, VDP, considered the demonstrated waterflood performance in each reservoir. The ultimate performance in each reservoir. The ultimate recovery was estimated by adding seven times the current annual production to the cumulative production (an assumed reserves-to-production ratio of 7 years), as long as the cumulative production was greater than 80% of the estimated ultimate recovery. The recovery efficiency is the estimated ultimate recovery divided by the OOIP. If the cumulative recovery was less than 80% of the ultimate, then the sum of the recovery factors for primary and secondary recovery reported by the operators was used as the ultimate recovery efficiency, if the information was available. The volumetric sweep efficiency was calculated from the recovery efficiency, FVF'S, initial oil saturation, and waterflood residual oil saturation (ROS). The endpoint mobility ratio was calculated from data-base or default values of viscosities and relative permeabilities. A pseudo-VDp was determined on the basis of pseudo-VDp was determined on the basis of the calculated sweep efficiency and mobility ratio for each reservoir in the data base that had sufficient data to perform these calculations. The pseudo-VDp correlations were based on results from a HigginsLeighton streamtube model of a five-spot pattern with 100 permeability layers, pattern with 100 permeability layers, assuming that the economic limit was reached at a producing WOR of 25. The median of all the calculated values was 0.72. The reservoirs for which insufficient data were available to calculate a value were assigned the median value of 0.72. If the pseudo-VDp value was calculated to he less than 0.5, it was given a default value of 0.5. This pseudo-VDp for each reservoir in the data pseudo-VDp for each reservoir in the data base was used in the predictive models for miscible and chemical EOR processes. The methodology the NPC used to calculate pseudo-VDp scales the EOR production to the waterflood volumetric sweep performance because it assumes that the geological performance because it assumes that the geological features that affect the waterflood will also affect the EOR process. Related papers: SPE 13239, SPE 13240, SPE 13241 Related discussions and replies:SPE 18397, SPE 20007, SPE 20009
- North America > United States > Texas > Permian Basin > Wolfcamp Formation (0.99)
- North America > United States > Texas > Permian Basin > Spraberry Formation (0.99)
- North America > United States > Texas > Permian Basin > Dean Formation (0.99)
- (7 more...)
Abstract The transport of sodium and calcium through porous media in the presence of clays and surfactant has been calculated. The exchange of the cations with both the clays and the surfactant micelles is assumed to result entirely from electrostatic association. The results show that a system in which the preflood, slug, and drive have the same sodium and calcium concentration can have a significant increase in the calcium concentration in the surfactant bank and a significant decrease in calcium concentration in the drive because of ion exchange. A process with a salinity gradient design can have a decrease in calcium concentration in the surfactant bank compared with the injected slug because of ion exchange. Introduction The exchange of sodium and calcium with clays is important to surfactant flooding because calcium has a much greater effect than sodium on the phase behavior and interfacial tension. This exchange phenomenon is well understood in the absence of surfactant. Experiments with surfactants have shown that the surfactants have a significant effect, but the interaction of the cations with them is not well understood. The previous works assumed that the flowing surfactant either was dissociated completely or formed a calcium complex of some form, independent of the sodium concentration. This work models the exchange of sodium and calcium with the micelles as if the association results entirely from electrostatic association. The calculations are compared with observations of corefloods. Assumptions A previous paper described the association of sodium and calcium with surfactant micelles. It was shown that the association can be described by electrostatic models such as the Donnan equilibrium model. It was shown that the "selectivity coefficient" with this model is not a constant but is only a weak function of the electrolyte composition at sufficiently high electrical potentials if the Stem layer thickness is large compared with the Debye-Huckel characteristic thickness of the electrical double layer. In this work it is assumed that the selectivity coefficient is directly proportional to the surfactant concentration but otherwise independent of the electrolyte composition. Further assumptions areco-ion exclusion is negligible, surfactant monomer concentration is negligible, dispersion is negligible, surfactant adsorption can be described by an adsorption isotherm that is dependent only on the surfactant concentration and the adsorbed surfactant associates sodium and calcium in the same way as the micelles, all anions other than the surfactant are treated as chloride ions, volume fraction of the flowing phase occupied by surfactant is small - i.e., the total concentration of unassociated ions per unit of pore volume is equal to the concentration of that ion in the electrolyte solution - and there is local equilibrium. Only single-phase flow is considered here. The presence of an oil phase will change the velocity of the waves and is described in Ref. 1. The Ion Exchange Equilibrium Relationships The Donnan equilibrium models is the stalling point for the models for association of sodium and calcium with both the clays and the micelles. The concentration of the associated species is denoted as C and C to represent the concentration of species i associated with the clays and micelles, respectively, expressed as equivalents per unit of pore volume. SPEJ P. 181^